## Mathematical Masterpieces: Further Chronicles by the ExplorersSpringer Science & Business Media, 2007年10月16日 - 340 頁 In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J. Gould writes: [W]e acquire a surprising source of rich and apparently limitless novelty from the primary documents of great thinkers throughout our history. But why should any nuggets, or even ?akes, be left for int- lectual miners in such terrain? Hasn’t the Origin of Species been read untold millions of times? Hasn’t every paragraph been subjected to overt scholarly scrutiny and exegesis? Letmeshareasecretrootedingeneralhumanfoibles. . . . Veryfew people, including authors willing to commit to paper, ever really read primary sources—certainly not in necessary depth and completion, and often not at all. . . . I can attest that all major documents of science remain cho- full of distinctive and illuminating novelty, if only people will study them—in full and in the original editions. Why would anyone not yearn to read these works; not hunger for the opportunity? [99, p. 6f] It is in the spirit of Gould’s insights on an approach to science based on p- mary texts that we o?er the present book of annotated mathematical sources, from which our undergraduate students have been learning for more than a decade. Although teaching and learning with primary historical sources require a commitment of study, the investment yields the rewards of a deeper understanding of the subject, an appreciation of its details, and a glimpse into the direction research has taken. Our students read sequences of primary sources. |

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algebraic algorithm approximate Archimedes arithmetic progressions arithmetical triangle Basel problem Bernoulli numbers binomial calculate Cardano circle claims coefficients compute convergence cube curved surface derivatives determine differential digit Disquisitiones division divisor problem divisors of numbers equation Euler example Exercise expression Fermat figurate numbers fluxional form x2 function fundamental theorem Gauss Gaussian curvature geometry given Huygens infinite integers iteration Lagrange Lagrange’s Legendre Legendre symbol Leonhard Euler linear manifold mathematicians mathematics measure of curvature modern modulo multiplied Newton nontrivial prime divisors notation number theory obtain odd prime osculating circle Pascal pattern pendulum perpendicular plane polynomial positive prime numbers proof prove quadratic forms quadratic reciprocity law quadratic residue quantity reader relatively prime Riemann root sequence Simpson's fluxional method solution solve sphere summation formula sums of powers synthetic division Tableau theorema egregium values

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第 5 頁 - If a straight line one extremity of which remains fixed be made to revolve at a uniform rate in a plane until it returns to the position from which it started, and if, at the same time as the straight line is revolving, a point move at a uniform rate along the straight line, starting from the fixed extremity, the point will describe a spiral in the plane.